Question

Prove the following
1.
Ans. ​

Answer 1

Answer:

cos²Φ/sinΦ+sinΦ=cosecΦ

LHS

=cos²Φ/sinΦ+sinΦ

=(cos²Φ+sin²Φ)/sinΦ

=1/sinΦ ( bcoz =cos²Φ+sin²Φ=1)

=cosecΦ

=RHS

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\frac{ { \cos}^{2} \theta }{ \sin\theta } + sin\theta = cosec\theta$

Taking L.H.S

$= \frac{ { \cos}^{2} \theta }{ \sin\theta } + sin\theta$

$= > \frac{ { \cos }^{2}\theta + { \sin}^{2} \theta }{ \sin\theta}$

$● { \sin}^{2}\theta + { \cos }^{2}\theta = 1$

$= > \frac{ 1}{ \sin\theta}$

$= > \frac{ 1}{ \sin\theta} = cosec\theta$

Hence proved

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